1. Field of the Invention
This invention relates to apparatus for computing transcendental functions quickly.
2. Description of Related Art
Computing transcendental functions by Taylor series generally requires one "add" instruction (which might take, for example, three clock times) and one "multiply" instruction (which might also take, for example, three more clock times) for each term. For processors computing transcendental functions to significant accuracy, it requires a number of terms to achieve a residual error less than the least significant bit of the answer. In a processor providing a floating point result having a 64-bit fraction, the number of terms is about ten for achieving 64-bit accuracy for the full range of an ordinary Taylor series; if multiply and add operations each take about three clock times, this would take about sixty clock times, which can be a significant amount of time when computation resources are at a premium. To obtain greater accuracy, even more terms and thus even more time would be required.
Accordingly, it would be advantageous to provide a technique for computing transcendental functions quickly. This advantage is achieved by apparatus according to the present invention in which terms of a Taylor series are computed in parallel and combined after parallel computation, so as to take only about one sixth of the "natural" amount of time per term.